Kinetic models evaluation for chemical organic matter removal prediction in a full-scale primary facultative pond treating municipal wastewater

Waste stabilization ponds (WSPs) as sanitation technologies are widely employed in small communities and developing countries because of their simplicity and low capital and operational expenditures (Butler et al. 2017; Passos et al. 2019). The system entirely contains natural processes and sub-processes in which wastewater is treated by biochemical reactions involving bacteria and algae (Faleschini et al. 2012). Facultative ponds (FPs) are characterized by shallow basins having an upper aerobic zone with available free-oxygen at the surface of the pond and a lower anaerobic zone with a lower depth area and no available free oxygen. The process is classified as primary facultative ponds (PFPs) and secondary facultative ponds (SFPs). The former receives raw wastewater (after preliminary treatment), whereas the latter receives pre-treated wastewater (typically the effluent from anaerobic lagoons) (Mara 2004).

FPs exhibit complex behavior in spite of being classified as simple and basic operational systems (Ho et al. 2017) because of the simultaneous existence of aerobic, facultative and anaerobic zones and the synergy and mutualistic relationship between photosynthetic algae/cyanobacteria and heterotrophic bacteria, which is the key feature inside the pond systems (Sah et al. 2011). Moreover, ponds are highly dynamic and subject to various operational and environmental parameters, which make the development of an all-encompassing model and forecasting the performance of the systems a challenge for designers (Sah et al. 2011; Alves et al. 2020).

A major concern/aim of treating wastewater in WSPs is organic matter removal. Chemical oxygen demand (COD) removal in the ponds may be attributed to several parameters such as temperature and detention time, which make the models susceptible to uncertainty, variability and complexity in integrating processes and sub-processes. Kinetic models have been introduced and used commonly to describe the removal of organic compounds in the stabilization ponds (Okoro & Nwaiwu 2017) and also, they can be used as a route to describe and predict the performance of biological treatment systems (Okoli & Okonkwo 2016). It is essential to understand the kinetics of pollutants in the system as it leads to proper design parameters and pond performance enhancement. Apart from many kinetic models available in literature, the most common models to describe WSPs is the first order kinetic model combined with plug flow and CSTR (continuous flow stirred tank reactors) regimes (Sun & Saeed 2009; Khosravi et al. 2013a). Also, the other kinetic models such as k–C*, Grau second-order and Stover–Kincannon models have been studied in the literature to determine their adaptability to find a relationship between the organic compounds at the inlet and outlet of WSPs. However, the main problem in replacing these models is that they are simplified and based on dependent mathematical relations. Therefore, selection of the best kinetic models for providing optimum design and predicting pollutant removal are vital to avoid malfunctions in different types of WSPs. Khosravi et al. (2013b) applied three models including the first-order substrate removal, Grau second-order and Stover-Kincannon models to determine the kinetic coefficients of sCOD (soluble COD) removal in WSP. The correlation coefficient was the highest for Stover-Kincannon Model (r² = 0.907), which represented the highest correlation between the values of influent and effluent in comparison with the other models. However, Gratziou & Chalatsi (2015) reported that the first order-plug flow (PF) constant rate provided the best mathematical relationship between the results and real data (r² > 0.80) for COD degradation compared to the other used models (first order-CSTR, K-C* and Stover-Kincannon models). The results of K-C* equation showed a promising result for modeling COD removal in stabilization ponds. Also, they concluded that reaction constant rates have a very strong relationship with hydraulic retention time. The prediction of removal rates of organic matter from WSPs at different retention times were studied by Okoro & Nwaiwu (2017) using first order, Monod, Grau and the Stover Kincannon models by fitting models to experimental data. Whereas the Stover Kincannon model showed a better adaptability (r²), the Grau model provides the best prediction of the substrate removal efficiency. Da Silva et al. (2010) compared the reaction constant rates of ideal first-order-PF model with the first order-CSTR model in six full-scale PFPs. They concluded that a PF regime with k = 0.013 day⁻¹ (r² = 0.96) provided a better fit than the CSTR flow pattern with k = 0.019 day⁻¹ (r² = 0.93). While it is very important to the design and sizing of the WSPs based on the knowledge of pollutant removal reaction rate constants (Gratziou & Chalatsi 2015), the comparative assessment of full-scale PFPs in the context of the reaction constants of organic matters biodegradation is very scarce as the literatures have mainly focused on the computation of the kinetic rates in the WSPs and the SFPs. A main knowledge gap in PFPs is to select the best model for mapping organic matter removal and predicting the behavior of the ponds. The gap will be addressed in this study by determining the different kinetic constant rates for organic matter removal and comparing the predictability powers of models.

The main objective of this study is to evaluate the adaptability of different kinetic models to link organic matter concentrations at the inlet and outlet and to compare the accuracy of COD removal prediction by kinetic models in a full-scale PFP as a secondary treatment of municipal wastewater on the basis of 3-year continuous operation. This investigation will help find the best kinetic models to design full-scale PFPs to achieve optimum sizing and predict the chemical organic matter concentrations of the effluent, which have not been discussed in the literature.

Esfarayen wastewater treatment plant (EWWTP), with an area of 33 ha located in the North-East of Iran. The region has two types of climates: temperate mountain climate and moderate, and warm and dry with mean annual precipitation and evaporation rates of 248 mm and 1,767 mm/year, respectively. The average monthly air temperature ranges from 2.8 °C to 27 °C. The first module has been in operation since 2000 with capacity of 4,000 m³/day and the existing nominal capacity of the plant is 8,000 m³/day with an area of about 20 ha. The plant receives domestic wastewater without agro-industrial liquid wastes. The pre-treatment units comprise mechanical and manual coarse screens and velocity-controlled grit chambers. The existing secondary treatment units consist of four PFPs operated in parallel, a maturation pond and chlorine contact basin (Figure 1). Design basis values of PFPs are also summarized in Table 1. The average organic loading rate is 200 kg BOD₅/ha·d which is in line with proposed values (100–400 kg BOD₅/ha·d) for designing PFPs to remove BOD on the basis of a relatively low surface loading (Shilton 2006).

Samples from the inlet and outlet of PFPs were weekly collected over a three-year period from January 2016 to December 2018 consisting of 141 data sets. Each data set of long-term sampling included flow rate, COD, biochemical oxygen demand (BOD₅), total suspended solids (TSS), volatile suspended solids (VSS), temperature, electrical conductivity (EC), and alkalinity at the inlet and COD, TSS, VSS, temperature, dissolved oxygen (DO) and alkalinity at the outlet. Samples were taken by 1.5 L plastic bottles rinsed by the effluent before sampling. Then, the bottles were labeled, sealed, stored away from the sunlight, transported on an ice chest to the laboratory located in EWWTP, and stored at 4 °C to be analyzed before 6 hours. The parameters were examined by the reference analytical procedures and protocols on the basis of the Standard Methods for the Examination of Water and Wastewater (APHA 2005). Organic matter was determined as COD (Jenway 6405 UV/VIS spectrophotometer, code: 5220-C) and BOD₅ (5-day BOD test, dilutions and DO electrode, code: 5210-B). TSS and volatile suspended solid (VSS) parameters were examined on the basis of oven-drying (Pat arya Sanat, Iran) at 103–105 °C and 550 °C, respectively (codes: 2540-D and 2540-E). EC was determined by electrometric method (HACH Lange HQ40D Multiparameter, code: 2510-B). Titration was also carried out to measure alkalinity (code: 2320).

A kinetic model simplifies the relationship of variables affecting COD removal in WSPs, which is applicable for the design of the units. Moreover, performance prediction and unit optimization are obtained by using chemical organic matter removal constant rates and their models. Substrate removal rate can be determined using first-order, Grau second-order and Stover–Kincannon models as the most fundamental and popular models (Abyar et al. 2017). As analytical models for the design of PFPs are on the basis of first-order kinetics and surface loading rate, the aerial first-order models were selected to be assessed. In addition to the first-order models, Grau second-order and Stover-Kincannon models are the fundamental ones to exhibit substrate removal rate in WSPs. The k–C* model was proposed by Kadlec & Knight (1996) to incorporate aerial loading rate, concentration at the inlet and outlet of the wetlands and a temperature-based kinetic rate in the wetlands. Since similar characteristics with wetlands can be seen in the pond systems such as no sludge removal throughout the operations, the performance of the k–C* model introduced for the modeling of wetlands can be used to predict the outlet of the ponds (Gratziou & Chalatsi 2015). To describe the chemical organic matter removal rate in PFP in this case study, five models including first-order models combined with PF and CSTR patterns, PF k–C*, Stover-Kincannon and Grau second-order models were used, compared and explained as follows:

The kinetic parameters K_B and U_max can be obtained by plotting Equation (8). By a plot of the inverse of the loading removal rate versus the inverse of the total loading rate, the parameters can be computed. Accordingly, a linear plot is obtained to determine (1/U_max) as the intercept of the plot and (K_B/U_max), which is the slope of the line.

The kinetic constant rates (m and n) are determined from the slope and intercept of the linear plot on the basis of Equation (10), respectively.

The statistical analyses were conducted using Microsoft Excel spreadsheet (Microsoft, 2010, USA). The software was also applied to calculate the outlet values obtained by bio-kinetic models. The error distribution was analyzed by using the ‘vegan’ package of the R software (version 3.0.3). To evaluate the differences between influent and effluent parameters, the statistical significance was determined by paired two-sample t-test with a significance level of p-value ≤0.05.

Table 2 shows the raw wastewater characteristics in EWWTP. The mean concentration of COD was 590 ± 141 mg/L ranging between 382 and 795 mg/L and influent BOD₅ concentration ranged between 176 and 380 mg/L with the average value of 263 mg/L. The mean BOD₅: COD ratio is 0.45 indicates the bio-treatability of sewage. Regarding suspended solids, the range of TSS concentrations was between 143 and 416 mg/L and VSS values ranged from 40 to 105 mg/L. The influent is classified as medium municipal wastewater in terms of organic matters while the sewage is characterized as low-strength wastewater in terms of the VSS parameter according to the recommended typical values of untreated domestic wastewater (Metcalf & Eddy 2003). The range of TSS values at the inlet is wide from low- to high-strength domestic sewage. The electrical conductivity (EC) of the wastewater was in the range of 1,546–2,480 μS/cm and the moderate EC values represent the presence of moderate amounts of dissolved inorganic substances in ionized form. The alkalinity level in the form of CaCO_­3 ranged between 520 and 840 mg/L showing alkaline character in the influent.

The treatment efficiencies of the PFP systems and effluent characteristics are summarized in Table 3 during three years of continuous operation. The results show that the mean effluent COD declined significantly up to 119 ± 52 mg/L (with a removal efficiency of 80%). The finding is consistent with the results presented by Alves et al. (2020), who reported the reduction of 69 to 82% of COD in the facultative ponds. Da Silva et al. (2010) also evaluated the performance of six full-scale PFPs, and they found that the average removal of unfiltered and filtered COD was equal to 50 and 83%, respectively.

The average removal efficiency of TSS was 59% with the effluent concentration of 92 ± 27 mg/L. The mean VSS concentration was almost halved from 62 ± 11 to 31 ± 5 mg/L with removal efficiency of 49%. The p-values in a paired two-sample t-test for COD, TSS and VSS concentration at inlet and outlet was near zero, presenting that the statistical difference between the concentrations at the inlet and outlet was extremely significant.

In terms of alkalinity, inlet concentration increased partially from 673 ± 70 to 688 ± 85 mg/L CaCO₃ with the p-value of 0.12, indicating a statistically insignificant difference. The mean values of temperatures at the inlet ranged between 12 to 28°C, while the effluent presented mean temperature in the range of 4 to 28°C. There was an increase in dissolved oxygen (DO) concentration from almost 0 to 1.2 mg/L. The enhancement in photosynthetic activity and reduction in organic matter concentration are the main reasons for the increase in DO concentrations (Martínez et al. 2014; Wallace et al. 2016).

The reaction constant rates of COD removal in the PFPs were determined using kinetic models including first order-PF, first order-CSTR, PF k–C*, Stover-Kincannon and Grau second-order models. After the statistical and mathematical processing of the collected data, the values of COD removal reaction rates were obtained from Equations (3)–(5), (8) and (10) and presented in Table 4. The correlation coefficient (r²) was used to select the most suitable and adoptable models (Yap et al. 2020).

The results showed that the all models, except the first order-CSTR with kinetic coefficient of 0.4509 m/d and r² = 0.3788, have relatively good performance (r² > 0.5). However, the Stover-Kincannon model provides better fitting (r² = 0.9294), which is consistent with the previous studies such as Yap et al. (2020), Okoro & Nwaiwu (2017) and Khosravi et al. (2013b). The linear regression of the kinetic reaction constants in the Stover-Kincannon model as the best fit for COD removal was shown in Figure 2. The calculated kinetic constants (U_max and K_B) were 80.65 g/L·d and 79.14 g/L·d according to the plot, respectively. One of the main reasons the Stover-Kincannon model showed higher adaptability in organic matter removal in pond systems is that it only measures the input against removal in a single volume (Hosseini & Borghei 2002). Therefore, the relationship shows a good adaptation especially for the systems with real scale and complicated reaction mechanisms that occur simultaneously such as suspended growth, sedimentation and adsorption. The Grau second-order model also showed a good adaptation and fitted well with data sets (r² = 0.6621) with the kinetic coefficients of m = 0.6725 and n = 15.867 d⁻¹. The values of kinetic coefficients for the combined model of first order-PF and the Kadlec and Knight model were 0.152 m/d and 0.1891 m/d with r² = 0.5759 and r² = 0.5173, respectively.

Table 5 shows the predicted effluent COD concentrations obtained by substituting the value of kinetic coefficients into equations in order to test the validity of the models. Moderate correlation values (0.6925, 0.6876, 0.6598, 0.6087 and 0.5216) obtained for Grau second-order, k–C*, first order-CSTR, first order-PF and Stover-Kincannon model, respectively. Figure 3 shows these correlation coefficients obtained by kinetic models for COD removal at the outlet of PFPs. Grau second-order model was found to be the best to predict the PFPs' performance in terms of COD removal. However, the performance of the model 1, model 2 and model 3 were still acceptable since no significant difference was observed between their accuracy.

The correlation coefficient of COD removal and comparison of measured and predicted COD values at the outlet of PFPs by the best model (Grau second-order model) is presented in Figure 4. Figure 4(a) shows that it is reasonable to use this model as a best fit line to predict COD removal. Also, Figure 4(b) shows insignificant difference between measured and predicted effluent COD values obtained by the second-order Grau model in most samples.

The performance accuracy of the models using different statistical indices is also compared in Table 6. The statistical metrics of kinetic models like ME and IA showed that the Grau second-order model predicted outlet COD removal more accurately compared to the other models (ME = 0.68 and IA = 0.91). In contrast, model 4 (Stover-Kincannon) offered the lowest precision with an ME value of 0.43 and IA equal to 0.76. Table 7 also shows the statistical indices of DR values calculated for the comparison of error distribution of values predicted by kinetic models. The results show that all models except the Grau second-order model generally predicted values lower than actual ones because the mean DR values are negative. Also, a narrower range of DR values was obtained in the K-C* and Grau models in contrast to the wide range of indexes, which can be seen in the Stover-Kincannon and the first-order models.

Moreover, the Gaussian function of DDR values was computed and represented in a standard normal distribution format. The standard normal distributions (QDDR) were computed for each model and then plotted in Figure 5. Generally, more tendencies in the error distribution graph to the centerline and the larger value of the maximum QDDR are equal to more accuracy (Noori et al. 2010). Model 3 (aerial K-C* model) and 5 (Grau model) provided the best accuracy in comparison with the other models in terms of DDR values referring to Figure 5. On the other hand, model 4 (Stover-Kincannon model) and model 2 (the first-order model coupled with CSTR flow pattern) represented lower accuracy for the prediction of outlet COD. In general, it could be inferred that the Grau second-order model can be used to predict effluent COD values with the highest precision while Stover-Kincannon model can be used to represent the real biological degradation that takes place during the treatment of wastewater by microorganisms in a PFP system treating municipal wastewater.

Table 8 provides the comparison of the reaction constant rates reported in the literature with the calculated kinetic constants in this study. It can be seen that the large variability in the kinetic rate constants of WSPs has been well documented in the literature. As can be seen in Table 8, the kinetic rates of organic matter degradation determined by different authors vary in a wide range because of a large number of characteristics presenting the complex web of interactions as well as external factors like weather conditions and detention time affecting the performance of the process.

Gratziou & Chalatsi (2015) compared three full scale WAP systems consisting of one facultative pond and one or two maturation ponds to treat municipal wastewater in North Greece. The computed COD removal rates of the first order PF model were equal to 0.0808, 0.0993 and 0.2492 m/d, which are relatively close to the values reported in this research (0.152 m/d). Da Silva et al. (2010) also proposed the reaction constant rates of 0.013 d⁻¹ for COD and 0.034 d⁻¹ for fCOD removal computed through the analysis of data collected from six full-scale PFP systems in Northeast Brazil treating domestic wastewater. The computed COD removal rate of the first order-CSTR model is 0.4509 m/d, which is higher than the values reported by Gratziou & Chalatsi (2015).

As mentioned before, the Stover-Kincannon model was the most suitable in describing the performance of the system whereas the Grau model predicts the efficiency of substrate removal more accurately. The result concurs with the values mentioned by Okoro & Nwaiwu (2017) and Khosravi et al. (2013b),. Applying this model by Okoro & Nwaiwu (2017) and Khosravi et al. (2013b), the kinetic rate constants were found to be (K_B = 0.118 g/L·d and U_max = 0.200 g/L·d) and (K_B = 128.5 g/L·d and U_max = 23.81 g/L·d), respectively. These kinetic coefficients were lower than the rates computed in this research (K_B = 79.14 g/L·d and U_max = 80.65 g/L·d), except K_B reported by Khosravi et al. (2013b), which may be attributed to the appropriate average temperature of effluent (18 °C) in the case study and high hydraulic retention time (HRT) (33 day). The close values of these constants calculated in this study shows that the process efficiency will decline as organic loading rate increases (Ahn & Forster 2000).

The Grau second-order model coefficients (m and n) for COD removal were 0.6725 and 15.867 d⁻¹, respectively, which are lower than the values reported by Khosravi et al. (2013b) (m = 5.091 and n = 39.28 d⁻¹). The values of m and n also were found to be 4.910 and 1.583 d⁻¹ by Okoro & Nwaiwu (2017) FPs with an HRT of 10 days, but the corresponding rates were 0.429 and 1.623 d⁻¹ in an anaerobic pond and 0.706 and 1.155 d⁻¹ in a maturation pond with the same HRT. The initial substrate concentration has positive effects on m value coefficient. The reported Grau second-order model coefficients in different studies are in a relatively wide range due to different substrate concentrations resulting from the stage of the treatment process. In the SFPs, biologically pre-treated effluent containing lower concentrations is treated whereas the raw wastewater characterized by higher organic matter concentrations is treated in PFPs.

Since the PFPs receive raw wastewater (as opposed to SFPs receiving pre-treated wastewater), the loading of organic matter obviously is greater than SFPs. As a result, in most cases but not all, the reaction constant rates/the substrate removal rate obtained in PFPs are higher than the values reported in the literature, which mainly indicate the kinetic rates in SFPs. The kinetic coefficients calculated in this study can be used as a quick reference to predict the performance efficiency of FPs in terms of COD removal for municipal or other wastewater types.

This research aims at evaluating the overall performance and determining the bio-kinetic coefficients of COD removal in PFPs employed as a secondary treatment of municipal wastewater. The removal efficiency of COD was found to be significant (80%) as the concentration declined from 590 to 119 mg/L. The differences between the concentration of TSS and VSS at the inlet and outlet were also extremely significant with the removal efficiency of 59 and 49%, respectively. Unlike many studies in which the SFPs were used to evaluate the kinetics of organic matter removal, the full-scale PFPs were used in this study to compare the predictive power of five kinetic models that have been applied widely to estimate the substrate removal rate.

While the Stover-Kincannon model offered better accuracy (r² = 0.9294) in comparison with the other models to define the system most appropriately, the Grau second-order model can be used to predict effluent COD values properly (r² = 0.6925). The maximum utilization rate (U_max) and saturation constant (K_B) were higher in this study compared to some studies that utilized SFPs, which may explain the higher values of the inlet chemical organic matters concentration. The kinetic rate constants (m and n) for Grau second-order model obtained in this research were 0.6725 and 15.867 d⁻¹, respectively which are relatively lower than the values (m = 5.091 and n = 39.28 d⁻¹) reported by Khosravi et al. (2013b) and much lower than ones found by Okoro & Nwaiwu (2017) for an SFP with the HRT of 10 days (4.910 and 1.583 d⁻¹). The difference between bio-kinetic rates reported in different literatures and ones found in this study is due to the stage of the process, which receives raw wastewater characterized by higher concentrations of organic matter.

The authors gratefully acknowledge deputy directors and operators in North Khorasan Province Water and Wastewater Company for their support during the study.

The authors declare no conflict of interest.

The research received no funds.

The authors declare no conflict of interest to any party.

All relevant data are included in the paper or its Supplementary Information.